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Parallel basis matrix triangularisation for hyper-sparse LP problems

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Contributed talk the IMA Conference on
Numerical Linear Algebra and Optimisation: 14th September 2007

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J. A. J. Hall

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Abstract

For linear programming (LP) problems where the revised simplex
method out-performs interior point methods, the pivotal column, shadow
prices and pivotal row are generally sparse. This property of LP
problems is referred to as hyper-sparsity. It will be shown that the
basis matrices of hyper-sparse LP problems are generally highly
reducible, and that the dominant cost of matrix inversion is that of
identifying the irreducible component via a triangularisation
procedure. This talk will describe such a procedure, discuss its
parallelisation and give results for both a serial simulation and a
prototype parallel implementation.

**Slides:**